Proton exchange membrane fuel cell nonlinear parameter estimation method based on preset time estimator

Abstract

The invention relates to the technical field of proton exchange membrane fuel cells, and discloses a method for estimating nonlinear parameters of a proton exchange membrane fuel cell based on a preset time estimator. According to the method, the output form of an electrochemical model of the proton exchange membrane fuel cell is converted into a linear system model through filtering operation, and a strong nonlinear system is rewritten into a linear parameterization form; a decoupled linearization system is obtained by defining an auxiliary variable and a decoupling algorithm, and the problem of system parameter coupling is solved; finally, preset time convergence of unknown nonlinear parameters in the model is achieved through a preset time parameter estimation method, online and rapid estimation of the nonlinear parameters of the proton exchange membrane fuel cell is achieved in the process, and the estimation speed of the nonlinear parameters is greatly increased; on-line estimation of unknown nonlinear parameters of the proton exchange membrane fuel cell can be realized only through input-output signals of an on-line measurement system.

Description

Technical Field

[0001] The invention relates to the technical field of proton exchange membrane fuel cells, in particular to a nonlinear parameter estimation method for proton exchange membrane fuel cells based on a preset time estimator. Background Art

[0002] In order to solve a series of pollution problems caused by excessive consumption of traditional fossil fuels, countries around the world have begun to vigorously develop clean alternative energy technologies to reduce damage to the environment. Among the many alternative energy technologies currently available, proton exchange membrane fuel cells have attracted widespread attention due to their high energy density, high thermal efficiency, and zero emission characteristics, and have been gradually applied to various industrial scenarios such as hydrogen-powered vehicles, hydrogen-powered transmission, and hydrogen-powered drones. An accurate mathematical model can reveal the operating mechanism of proton exchange membrane fuel cells and provide guidance for subsequent control research and optimization design. Therefore, it is of great significance to achieve online and accurate estimation of unknown parameters in the proton exchange membrane mathematical model, thereby improving the accuracy of its mathematical model.

[0003] In the mathematical model of proton exchange membrane fuel cells, the system exhibits strong nonlinearity, and some unknown parameters are embedded in the nonlinear terms. Existing engineering methods usually use adaptive parameter estimation methods or intelligent algorithms to estimate unknown parameters, but traditional adaptive parameter estimation methods are difficult to apply to strongly nonlinear proton exchange membrane fuel cell systems and have the problem of low convergence accuracy; while methods that rely on intelligent algorithms have the problems of long calculation time, inability to achieve online parameter estimation, and local convergence, and are not suitable for proton exchange membrane fuel cell systems. Summary of the invention

[0004] 1. Technical issues to be resolved

[0005] In view of the deficiencies in the prior art, the present invention provides a proton exchange membrane fuel cell nonlinear parameter estimation method based on a preset time estimator, which has the advantages of online and accurate estimation of unknown nonlinear parameters in proton exchange membrane fuel cells, and solves the above technical problems.

[0006] (II) Technical solution

[0007] To achieve the above object, the present invention provides the following technical solution: a nonlinear parameter estimation method for a proton exchange membrane fuel cell based on a preset time estimator, comprising the following steps:

[0008] S1. establishing a proton exchange membrane fuel cell electrochemical model, and rewriting the established proton exchange membrane fuel cell electrochemical model into an output form to obtain a changed proton exchange membrane fuel cell electrochemical model;

[0009] The specific expression of the established proton exchange membrane fuel cell electrochemical model is as follows:

[0010] V fc =n cell (Ev act -v ohm -v conc )

[0011] Among them, V fc Represents the output voltage of the battery, n cell Indicates the number of cells, E indicates the open circuit voltage of the battery, v ohm Represents the ohmic voltage drop of the battery, v conc represents the concentration pressure drop of the fuel cell, v act Indicates the activation voltage drop of the battery;

[0012] The electrochemical model of the proton exchange membrane fuel cell is rewritten into an output form including: using the battery output voltage V fc As the system output y, the battery current I st As the system input u, the unknown parameters a and b are selected as the unknown parameters to be estimated, and the expression of the changed proton exchange membrane fuel cell electrochemical model is obtained as follows:

[0013]

[0014] Wherein, h1 represents the first known part, h2 represents the second known part, h3 represents the third known part, h4 represents the fourth known part, e represents a natural constant, θ1 represents the first parameter to be estimated, θ1=a, θ2 represents the second parameter to be estimated, θ2=b;

[0015] S2. Performing a filtering operation on the changed electrochemical model of the proton exchange membrane fuel cell to obtain a linearized system model, and defining auxiliary variables and a decoupling algorithm for the linearized system model to obtain a decoupled linearized system;

[0016] In step S2, the changed electrochemical model of the proton exchange membrane fuel cell is filtered to obtain a specific expression of the linearized system model as follows:

[0017] Y ef =Φ l (t)G(θ)

[0018] Among them, Y ef represents the linearized system output obtained by filtering, Φ l (t)∈R 1×3 represents the regression vector of the linearized system, R 1×3 Represents a matrix with a dimension of 1×3, G(θ)∈R 3×1 represents the unknown parameter vector of the expansion, R 3×1 Indicates that the dimension of the matrix is ​​3×1;

[0019] The specific expression of the decoupled linearized system is as follows:

[0020] M(t)=Δ(t)G(θ)

[0021] Where M(t) represents the decoupled linearized system, M(t)∈R 3×1 , R 3×1 The dimension of the matrix is ​​3×1, and M(t) = αdj{P(t)}Q(t), αdj{P(t)} represents the adjoint matrix of the auxiliary matrix P(t), αdj{P(t)}∈R 3×3 , R 3×3 Indicates that the dimension of the matrix is ​​3×3, Δ(t) represents the determinant of the auxiliary matrix P(t), that is, Δ(t)=det{P(t)}, det{P(t)} represents the calculation of the determinant of the auxiliary matrix P(t), and t represents the time variable;

[0022] S3, setting a preset time parameter estimator for the decoupled linearized system obtained in step S2, and estimating the preset time parameter of the unknown nonlinear parameter based on the estimated parameter value, the specific expression of which is as follows:

[0023]

[0024] in, represents the estimated value of the unknown parameter vector θ, represents the first-order derivative of the estimate of the unknown parameter vector θ, R 2×1 Indicates that the dimension of the matrix is ​​2×1, R 2×1 Indicates that the dimension of the matrix is ​​2×1, T p represents the convergence time preset by the user, t represents the time variable, Γ represents the gain matrix of the system, Γ∈R 2×2 , R 2×2 The dimension of the matrix is ​​2×2, C represents the screening matrix of the adaptive law, C∈R 2×3 , R 2×3 indicates that the dimension of the matrix is ​​2×3, W(t) indicates the defined auxiliary matrix, Δ(t) indicates the determinant of the auxiliary matrix P(t), represents the estimated value of the expanded unknown parameter vector, R 3×1 This means that the dimension of the matrix is ​​3×1.

[0025] As a preferred technical solution of the present invention, the activation voltage drop v of the battery in step S1 is act The specific expression is as follows:

[0026] v act =v0+va (1-e bi )

[0027] Where v0 represents the voltage drop at zero current density, v a represents the activation coefficient of the battery, e represents the natural constant, b represents the unknown parameter that affects the accuracy of the electrochemical model, and i represents the current density of the battery. The specific expression is as follows:

[0028]

[0029] Among them, I st Indicates the input current of the battery, A fc Indicates the active area of ​​the battery;

[0030] The expression of the voltage drop v0 at zero current density is as follows:

[0031]

[0032] Where a represents the unknown parameter that affects the accuracy of the electrochemical model, T fc Indicates the battery temperature, p ca Expressed as the battery cathode pressure, p sat represents the battery saturated vapor pressure, and ln represents the logarithmic function with the natural constant e as the base.

[0033] As a preferred technical solution of the present invention, the linearized system output Y obtained by filtering ef The expression is as follows:

[0034]

[0035] in, The linearized system output Y is obtained by filtering. ef The first-order derivative of , s represents the differential operator, and λ represents the filter coefficient Y ef represents the linearized system output obtained by filtering, y represents the system output, h1 represents the first known part, and h3 represents the third known part.

[0036] As a preferred technical solution of the present invention, the regression vector Φ of the linearized system l The expression of (t) is as follows:

[0037] Φ l (t) = [φ 1f ,φ 2f ,φ 3f ]

[0038]

[0039] Among them, φ 1frepresents the first element of the regression vector, t represents the time variable, represents the first-order derivative of the first element of the regression vector, h2 represents the second known part, h3 represents the third known part, s represents the differential operator, φ 2f represents the second element of the regression vector, represents the first derivative of the second element of the regression vector, φ 3f represents the third element of the regression vector, represents the first derivative of the third element of the regression vector, A fc represents the activated area of ​​the battery, h1 represents the first known part, h2 represents the second known part, h3 represents the third known part, represents the first-order derivative of the system input u;

[0040] The expression of the extended unknown parameter vector G(θ) is as follows:

[0041] G(θ)=[θ1,θ2,θ1θ2] T

[0042] Among them, θ represents the unknown parameter vector, θ∈R 2×1 , θ=[θ1,θ2] T , R 2×1 The dimension of the matrix is ​​2×1, θ1 represents the first parameter to be estimated, θ2 represents the second parameter to be estimated, and the superscript T represents transposition;

[0043] The auxiliary variables include two auxiliary matrices P(t) and Q(t), and their specific expressions are as follows:

[0044]

[0045] Among them, P(t) and Q(t) represent two auxiliary matrices, represents the first-order derivative of the auxiliary matrix P(t), Φ l (t) represents the regression vector of the linearized system, t represents the time variable, Represents the filter coefficient, the superscript T represents the transposition, and Y ef (t) represents the linearized system output obtained by filtering.

[0046] As a preferred technical solution of the present invention, the specific expression of the first known part h1 in step S1 is as follows:

[0047]

[0048] The specific expression of the second known part h2 in step S1 is as follows:

[0049] h2=-n cell

[0050] The specific expression of the third known part h3 in step S1 is as follows:

[0051] h3=n cell v a

[0052] The specific expression of the fourth known part h4 in step S1 is as follows:

[0053]

[0054] Among them, h1 represents the first known part, h2 represents the second known part, h3 represents the third known part, h4 represents the fourth known part, u represents the system input, n cell Indicates the number of cells, E indicates the open circuit voltage of the battery, v ohm Represents the ohmic voltage drop of the battery, v conc represents the concentration pressure drop of the fuel cell, v act Indicates the activation voltage drop of the battery, T fc Indicates the battery temperature, p ca Expressed as the battery cathode pressure, p sat represents the battery saturated vapor pressure, and ln represents the logarithmic function with the natural constant e as the base.

[0055] Compared with the prior art, the present invention provides a nonlinear parameter estimation method for a proton exchange membrane fuel cell based on a preset time estimator, which has the following beneficial effects:

[0056] The present invention converts the output form of the electrochemical model of the proton exchange membrane fuel cell into a linearized system model through a filtering operation, and rewrites the strong nonlinear system into a linear parameterized form; then, by defining auxiliary variables and a decoupling algorithm, a decoupled linearized system is obtained, and the problem of system parameter coupling is solved; finally, a preset time convergence of unknown nonlinear parameters in the model is achieved through a preset time parameter estimation method, and this process realizes online and fast estimation of the nonlinear parameters of the proton exchange membrane fuel cell, greatly improving the estimation speed of the nonlinear parameters; and it can realize online estimation of the unknown nonlinear parameters of the proton exchange membrane fuel cell only by measuring the input-output signal of the system online. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 A schematic diagram of a preset time estimator of the present invention;

[0058] Figure 2 A schematic diagram of the battery structure of a proton exchange membrane fuel cell of the present invention;

[0059] Figure 3 It is a schematic diagram of the nonlinear parameter estimation result of the present invention;

[0060] Figure 4 Schematic diagram for comparing voltage restoration in the system of the present invention. DETAILED DESCRIPTION

[0061] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0062] See also Figure 1-4 , a nonlinear parameter estimation method for a proton exchange membrane fuel cell based on a preset time estimator comprises the following steps:

[0063] S1. establishing a proton exchange membrane fuel cell electrochemical model, and rewriting the established proton exchange membrane fuel cell electrochemical model into an output form to obtain a changed proton exchange membrane fuel cell electrochemical model;

[0064] The specific expression of the established proton exchange membrane fuel cell electrochemical model is as follows:

[0065] V fc =n cell (Ev act -v ohm -v conc )

[0066] Among them, V fc Represents the output voltage of the battery, n cell Indicates the number of cells, E indicates the open circuit voltage of the battery, v ohm Represents the ohmic voltage drop of the battery, v conc represents the concentration pressure drop of the fuel cell, v act Indicates the activation voltage drop of the battery. In this simulation experiment, n is set cell =8. The activation voltage drop v of the battery in step S1 act The specific expression is as follows:

[0067] v act =v0+v a (1-e bi )

[0068] Where V0 represents the voltage drop at zero current density, v a represents the activation coefficient of the battery, e represents the natural constant, and b represents the unknown parameter that affects the accuracy of the electrochemical model. In this simulation experiment, b=-18 is set. i represents the current density of the battery, and its specific expression is as follows:

[0069]

[0070] Among them, I st Indicates the input current of the battery, A fc Represents the activation area of ​​the battery. In this simulation experiment, I st =60+2sin(2πt);

[0071] The expression of voltage drop v0 at zero current density is as follows:

[0072]

[0073] Where a represents the unknown parameter that affects the accuracy of the electrochemical model, T fc Indicates the battery temperature, p ca Expressed as the battery cathode pressure, p sat represents the battery saturated vapor pressure, ln represents the logarithmic function with the natural constant e as the base. In this simulation experiment, a=0.1148, T fc =80℃;

[0074] The electrochemical model of the proton exchange membrane fuel cell is rewritten into an output form including: using the battery output voltage V fc As the system output y, the battery current I st As the system input u, the unknown parameters a and b are selected as the unknown parameters to be estimated, and the expression of the changed proton exchange membrane fuel cell electrochemical model is obtained as follows:

[0075]

[0076] Wherein, h1 represents the first known part, h2 represents the second known part, h3 represents the third known part, h4 represents the fourth known part, e represents a natural constant, θ1 represents the first parameter to be estimated, θ1=a, θ2 represents the second parameter to be estimated, θ2=b;

[0077] The specific expression of the first known part h1 is as follows:

[0078]

[0079] The specific expression of the second known part h2 is as follows:

[0080] h2=-n cell

[0081] The specific expression of the third known part h3 is as follows:

[0082] h3=n cell v a

[0083] The specific expression of the fourth known part h4 is as follows:

[0084]

[0085] Among them, h1 represents the first known part, h2 represents the second known part, h3 represents the third known part, h4 represents the fourth known part, u represents the system input, n cell Indicates the number of cells, E indicates the open circuit voltage of the battery, v ohm Represents the ohmic voltage drop of the battery, v conc represents the concentration pressure drop of the fuel cell, v act Indicates the activation voltage drop of the battery, T fc Indicates the battery temperature, p ca Expressed as the battery cathode pressure, p sat represents the battery saturated vapor pressure, ln represents the logarithmic function with the natural constant e as the base;

[0086] S2. Performing a filtering operation on the changed electrochemical model of the proton exchange membrane fuel cell to obtain a linearized system model, and defining auxiliary variables and a decoupling algorithm for the linearized system model to obtain a decoupled linearized system;

[0087] In step S2, a filtering operation is performed on the changed electrochemical model of the proton exchange membrane fuel cell to obtain a specific expression of the linearized system model as follows:

[0088] Y ef =Φ l (t)G(θ)

[0089] Among them, Y ef represents the linearized system output obtained by filtering, Φ l (t)∈R 1×3 represents the regression vector of the linearized system, R 1×3 Represents a matrix with a dimension of 1×3, G(θ)∈R 3×1 represents the unknown parameter vector of the expansion, R 3×1 Indicates that the dimension of the matrix is ​​3×1;

[0090] The regression vector Φ of the linearized system l The expression of (t) is as follows:

[0091] Φ l (t) = [φ 1f ,φ 2f ,φ 3f ]

[0092]

[0093] Among them, φ 1frepresents the first element of the regression vector, t represents the time variable, represents the first-order derivative of the first element of the regression vector, h2 represents the second known part, h3 represents the third known part, s represents the differential operator, φ 2f represents the second element of the regression vector, represents the first derivative of the second element of the regression vector, φ 3f represents the third element of the regression vector, represents the first derivative of the third element of the regression vector, A fc represents the activated area of ​​the battery, h1 represents the first known part, h2 represents the second known part, h3 represents the third known part, represents the first-order derivative of the system input u;

[0094] The linearized system output Y obtained by filtering ef The expression is as follows:

[0095]

[0096] in, The linearized system output Y is obtained by filtering. ef The first-order derivative of , s represents the differential operator, and λ represents the filter coefficient Y ef represents the linearized system output obtained by filtering, y represents the system output, h1 represents the first known part, and h3 represents the third known part;

[0097] The specific expression of the decoupled linearized system is as follows:

[0098] M(t)=Δ(t)G(θ)

[0099] Where M(t) represents the decoupled linearized system, M(t)∈R 3×1 , R 3×1 The dimension of the matrix is ​​3×1, and M(t) = αdj{P(t)}Q(t), αdj{P(t)} represents the adjoint matrix of the auxiliary matrix P(t), αdj{P(t)}∈R 3×3 , R 3×3 Indicates that the dimension of the matrix is ​​3×3, Δ(t) represents the determinant of the auxiliary matrix P(t), that is, Δ(t)=det{P(t)}, det{P(t)} represents the calculation of the determinant of the auxiliary matrix P(t), and t represents the time variable;

[0100] The expression of the expanded unknown parameter vector G(θ) is as follows:

[0101] G(θ)=[θ1,θ2,θ1θ2] T

[0102] Among them, θ represents the unknown parameter vector, θ∈R 2×1 , θ=[θ1,θ2] T , R 2×1 The dimension of the matrix is ​​2×1, θ1 represents the first parameter to be estimated, θ2 represents the second parameter to be estimated, and the superscript T represents the transpose. In this simulation experiment, the theoretical parameter to be estimated θ = [0.1148 -18] T , set λ = 0.0333;

[0103] Auxiliary variables include two auxiliary matrices P(t) and Q(t), and their specific expressions are as follows:

[0104]

[0105] Among them, P(t) and Q(t) represent two auxiliary matrices, represents the first-order derivative of the auxiliary matrix P(t), Φ l (t) represents the regression vector of the linearized system, t represents the time variable, Represents the filter coefficient, the superscript T represents the transposition, and Y ef (t) represents the linearized system output obtained by filtering;

[0106] S3, setting a preset time parameter estimator for the decoupled linearized system obtained in step S2, and estimating the preset time parameter of the unknown nonlinear parameter based on the estimated parameter value, the specific expression of which is as follows:

[0107]

[0108] in, represents the estimated value of the unknown parameter vector θ, represents the first-order derivative of the estimate of the unknown parameter vector θ, R 2×1 Indicates that the dimension of the matrix is ​​2×1, R 2×1 Indicates that the dimension of the matrix is ​​2×1, T p represents the convergence time preset by the user, t represents the time variable, Γ represents the gain matrix of the system, Γ∈R 2×2 , R 2×2 The dimension of the matrix is ​​2×2, C represents the screening matrix of the adaptive law, C∈R 2×3 , R 2×3 indicates that the dimension of the matrix is ​​2×3, W(t) indicates the defined auxiliary matrix, Δ(t) indicates the determinant of the auxiliary matrix P(t), represents the estimated value of the expanded unknown parameter vector, R 3×1 The dimension of the matrix is ​​3×1. In this simulation experiment, we set T p=15s,Γ=diag[1×10 13 4×10 8 ], diag represents a diagonal matrix.

[0109] This method uses only measurable system input and output signals, introduces filtering and auxiliary variables to design a nonlinear preset time adaptive law, and realizes online and accurate estimation of proton exchange membrane fuel cells. At the same time, the application of the above technical solution shows that the present invention realizes the preset time parameter estimation of unknown nonlinear parameters of proton exchange membrane fuel cells, broadens the application scenarios of adaptive algorithms, and greatly shortens the convergence time of parameter estimation.

[0110] Figure 2 This is the schematic diagram of the proton exchange membrane fuel cell system. It can be seen that the proton exchange membrane fuel cell is mainly composed of three parts: an anode for hydrogen, a cathode for air, and a proton exchange membrane. The hydrogen at the anode undergoes a redox reaction with the oxygen at the cathode to generate an electromotive force to drive an external load. The hydrogen ions generated by the decomposition of hydrogen pass through the proton exchange membrane to the cathode, and the generated electrons are transmitted to the cathode through the external load. Finally, the two combine with oxygen in the air to generate water. Unreacted hydrogen will be discharged from the anode outlet of the fuel cell, and the water produced by the reaction will be discharged from the cathode outlet of the battery together with the unreacted air.

[0111] Figure 3-4 This is a simulation verification diagram of a nonlinear parameter estimation method with preset time designed according to the present invention for a proton exchange membrane fuel cell system. Figure 3 This is the result diagram of nonlinear parameter estimation. It can be seen that the estimated values ​​of the unknown parameters converged to the true value at the user-preset convergence time point (15 seconds), and the parameter estimation error achieved convergence within the preset time. Figure 4 This is a comparison chart of system voltage restoration performance. It can be seen that when the estimated value of the unknown parameter is brought back to the original system, the original system can be restored correctly, ensuring the accuracy of the model.

[0112] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A nonlinear parameter estimation method for a proton exchange membrane fuel cell based on a preset time estimator, characterized in that: The following steps are involved: S1. establishing a proton exchange membrane fuel cell electrochemical model, and rewriting the established proton exchange membrane fuel cell electrochemical model into an output form to obtain a changed proton exchange membrane fuel cell electrochemical model; The specific expression of the established proton exchange membrane fuel cell electrochemical model is as follows: V fc =n cell (Ev act -v ohm -v conc ) Among them, V fc Represents the output voltage of the battery, n cell Indicates the number of cells, E indicates the open circuit voltage of the battery, v ohm Represents the ohmic voltage drop of the battery, v conc represents the concentration pressure drop of the fuel cell, v act Indicates the activation voltage drop of the battery; The electrochemical model of the proton exchange membrane fuel cell is rewritten into an output form including: using the battery output voltage V fc As the system output y, the battery current I st As the system input u, the unknown parameters a and b are selected as the unknown parameters to be estimated, and the expression of the changed proton exchange membrane fuel cell electrochemical model is obtained as follows: Wherein, h1 represents the first known part, h2 represents the second known part, h3 represents the third known part, h4 represents the fourth known part, e represents a natural constant, θ1 represents the first parameter to be estimated, θ1=a, θ2 represents the second parameter to be estimated, θ2=b; S2. Performing a filtering operation on the changed electrochemical model of the proton exchange membrane fuel cell to obtain a linearized system model, and defining auxiliary variables and a decoupling algorithm for the linearized system model to obtain a decoupled linearized system; In step S2, the changed electrochemical model of the proton exchange membrane fuel cell is filtered to obtain a specific expression of the linearized system model as follows: Y ef =Φ l (t)G(θ) Among them, Y ef represents the linearized system output obtained by filtering, Φ l (t)∈R 1×3 represents the regression vector of the linearized system, R 1×3 Represents a matrix with a dimension of 1×3, G(θ)∈R 3×1 represents the unknown parameter vector of the expansion, R 3×1 Indicates that the dimension of the matrix is ​​3×1; The specific expression of the decoupled linearized system is as follows: M(t)=Δ(t)G(θ) Where M(t) represents the decoupled linearized system, M(t)∈R 3×1 , R 3×1 The dimension of the matrix is ​​3×1, and M(t) = αdj{P(t)}Q(t), αdj{P(t)} represents the adjoint matrix of the auxiliary matrix P(t), αdj{P(t)}∈R 3×3 , R 3×3 Indicates that the dimension of the matrix is ​​3×3, Δ(t) represents the determinant of the auxiliary matrix P(t), that is, Δ(t)=det{P(t)}, det{P(t)} represents the calculation of the determinant of the auxiliary matrix P(t), and t represents the time variable; S3, setting a preset time parameter estimator for the decoupled linearized system obtained in step S2, and estimating the preset time parameter of the unknown nonlinear parameter based on the estimated parameter value, the specific expression of which is as follows: in, represents the estimated value of the unknown parameter vector θ, represents the first-order derivative of the estimate of the unknown parameter vector θ, R 2×1 Indicates that the dimension of the matrix is ​​2×1, R 2×1 Indicates that the dimension of the matrix is ​​2×1, T p represents the convergence time preset by the user, t represents the time variable, Γ represents the gain matrix of the system, Γ∈R 2×2 , R 2×2 The dimension of the matrix is ​​2×2, C represents the screening matrix of the adaptive law, C∈R 2×3 , R 2×3 indicates that the dimension of the matrix is ​​2×3, W(t) indicates the defined auxiliary matrix, Δ(t) indicates the determinant of the auxiliary matrix P(t), represents the estimated value of the expanded unknown parameter vector, R 3×1 This means that the dimension of the matrix is ​​3×1.

2. The nonlinear parameter estimation method for proton exchange membrane fuel cell based on a preset time estimator according to claim 1, characterized in that: The activation voltage drop v of the battery in step S1 act The specific expression is as follows: v act =v0+v a (1-e bi ) Where v0 represents the voltage drop at zero current density, v a represents the activation coefficient of the battery, e represents the natural constant, b represents the unknown parameter that affects the accuracy of the electrochemical model, and i represents the current density of the battery. The specific expression is as follows: Among them, I st Indicates the input current of the battery, A fc Indicates the active area of ​​the battery; The expression of the voltage drop v0 at zero current density is as follows: Where a represents the unknown parameter that affects the accuracy of the electrochemical model, T fc Indicates the battery temperature, p ca Expressed as the battery cathode pressure, p sat represents the battery saturated vapor pressure, and ln represents the logarithmic function with the natural constant e as the base.

3. The nonlinear parameter estimation method for proton exchange membrane fuel cell based on a preset time estimator according to claim 1, characterized in that: The linearized system output Y obtained by filtering ef The expression is as follows: in, The linearized system output Y is obtained by filtering. ef The first-order derivative of , s represents the differential operator, and λ represents the filter coefficient Y ef represents the linearized system output obtained by filtering, y represents the system output, h1 represents the first known part, and h3 represents the third known part.

4. The nonlinear parameter estimation method for proton exchange membrane fuel cell based on a preset time estimator according to claim 1, characterized in that: The regression vector Φ of the linearized system l The expression of (t) is as follows: F l (t)=[φ 1f ,f 2f ,f 3f ] Among them, φ 1f represents the first element of the regression vector, t represents the time variable, represents the first derivative of the first element of the regression vector, h2 represents the second known part, h3 represents the third known part, s represents the differential operator, φ 2f represents the second element of the regression vector, represents the first derivative of the second element of the regression vector, φ 3f represents the third element of the regression vector, represents the first derivative of the third element of the regression vector, A fc represents the activated area of ​​the battery, h1 represents the first known part, h2 represents the second known part, h3 represents the third known part, represents the first-order derivative of the system input u; The expression of the extended unknown parameter vector G(θ) is as follows: G(θ)=[θ1,θ2,θ1θ2] T Among them, θ represents the unknown parameter vector, θ∈R 2×1 , θ=[θ1,θ2] T , R 2×1 The dimension of the matrix is ​​2×1, θ1 represents the first parameter to be estimated, θ2 represents the second parameter to be estimated, and the superscript T represents transposition; The auxiliary variables include two auxiliary matrices P(t) and Q(t), and their specific expressions are as follows: Among them, P(t) and Q(t) represent two auxiliary matrices, represents the first-order derivative of the auxiliary matrix P(t), Φ l (t) represents the regression vector of the linearized system, t represents the time variable, l represents the filter coefficient, the superscript T represents the transposition, and Y ef (t) represents the linearized system output obtained by filtering.

5. The nonlinear parameter estimation method for proton exchange membrane fuel cell based on a preset time estimator according to claim 1, characterized in that: The specific expression of the first known part h1 in step S1 is as follows: The specific expression of the second known part h2 in step S1 is as follows: h2=-n cell The specific expression of the third known part h3 in step S1 is as follows: h3=n cell v a The specific expression of the fourth known part h4 in step S1 is as follows: Among them, h1 represents the first known part, h2 represents the second known part, h3 represents the third known part, h4 represents the fourth known part, u represents the system input, n cell Indicates the number of cells, E indicates the open circuit voltage of the battery, v ohm Represents the ohmic voltage drop of the battery, v conc represents the concentration pressure drop of the fuel cell, v act Indicates the activation voltage drop of the battery, T fc Indicates the battery temperature, p ca Expressed as the battery cathode pressure, p sat represents the battery saturated vapor pressure, and ln represents the logarithmic function with the natural constant e as the base.

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